How does string field theory differ from string theory

String theory as it has developed is not a field theory. It has more in common with Schroedinger's or Dirac's particle theories than with QED or the Standard Model. There is a real string field theory, and papers about it sometime appear on the arxiv. It started with Sen's conjectures about the role of tachyons and has developed over a number of years.

I am interested that Kaku claims an interest here. I don't know of any thread in the research I have seen that goes back to him, but of course that doesn't mean it isn't there.

I don't know if what I have to say on the subject is really meaningful to you or not, but I'll give it a try.

String theory, whether formulated as a field theory or not, is a largely philosophical theory. There is no evidence to support the theory whatsoever. It is largely its philosophical and mathematical consistency and dominance that provides the support it receives. String theory is first and foremost a holistic theory, while field theories dominate today, they are notably less holistic than other theories.

A recent discovery has been that the entropy of information is proportional to the surface area. What this implies is that one of the four dimensions is illusory, and the infinities of field theory are as well. For more information I suggest you check last months issue of Scientific American.

In reply to Wuliheron, that is the entropy content of a black hole which is proportional to the area of its event horizon. And that fact was discovered by string theory. Your "no evidence" jibe is way behind the times.

As I said on the other thread, it has made the prediction that the entropy of a black hole is proportional to the surfqace area of its event horizon, and has given a bottom-up derivation of the Beckenstein-Hawking entropy formula.

Originally posted by selfAdjoint As I said on the other thread, it has made the prediction that the entropy of a black hole is proportional to the surface area of its event horizon, and has given a bottom-up derivation of the Beckenstein-Hawking entropy formula.

It was my understanding that the derivation was for the special case of extremal or near-extremal black holes.

I gather that the entropy is calculated for a system of D-branes with gravity turned off (settinhg gstring equal to zero) ---the system of D-branes represents the extremal black hole by having the same quantum numbers----and it is conjectured but unproven that turning gravity back on (returning gstring to its correct level)

An extremal black hole is one that is electrically charged and charged to maximum theoretically possible charge (charge = mass in natural units).

thus an extremal black hole is not your usual generic BH that one either gets in observational astronomy or ordinarily thinks about.

There is an interesting discussion of the string theory result on BH entropy in a 2003 paper by
Smolin http://arxiv.org/hep-th/0303185 [Broken] page 39 and then again middle of page 61
One of his references is to a 2001 review of string theory results about BH by
S. Das and S. Mathur
http://arxiv.org/gr-qc/0105063 [Broken]
Either one might be helpful in clarifying what exactly has been proven in the string theory
context, and in which special cases, concerning BH entropy
If you know of a more recent survey than these two please post the link as it would
be interesting to compare with Ashtekar, Baez, Corichi, Krasnov 1997 result which extends
to black holes in general.

It will only become testable when we can observe a black hole (not necessarily up close). Nevertheless it is a definitie prediction which agrees with the semiclassical calculation of Hawking and Beckenstein. I am given to understand that although the original result was confined to extremal black holes, it has since been extended to more general cases.

Originally posted by selfAdjoint
Marcus, I will look at the papers you linked.

selfAdjoint,
I cant vouch for the 2001 paper by Das and Mathur
It is however a recent survey paper titled
"The Quantum Physics of Black Holes: Results from String Theory"

and it is one of several string theory papers that Smolin refers to.

I looked at it briefly but could not get well enough oriented to find
what I was looking for----you might find it helpful though I did not.

In the Smolin paper, what he has to say on the subject is really concentrated on page 39.

And indeed what you say seems right about the result being extended,
the question is by how much, to include which cases.
You and Smolin are in agreement on the general fact of the result
having been extended to a larger class than strictly extremal.
Maybe I will quote an exerpt of page 39 here to save anyone else the
trouble of downloading----the whole article (a comparison of results in
LQG and String Theory) is 90 pages so takes several miniutes to get down.

Originally posted by selfAdjoint ...agrees with the semiclassical calculation of Hawking and Beckenstein. I am given to understand that although the original result was confined to extremal black holes, it has since been extended to more general cases.

Here's a quote from page 39 of http://arxiv.org/hep-th/0303185 [Broken]
giving some idea of the extent to which the result has been made to cover other cases
(the extension has been confined to the extremal "neighborhood"----not enough, it would seem, to cover certain ordinary cases)

-----------
"6.3 Results and conjectures concerning black holes

String theory also has led to results which are relevant for the understanding of black holes.
To express them one has to know that in the state space of a supersymmetric theory there
is a subspace in which a fraction of the supersymmetry transformations are broken, leaving
still unbroken a number of supersymmetries at least twice the dimension of the spinors in
that dimension. These are known as BPS states...
Classical supergravity has BPS states (i.e. classical solutions), among which are black
holes whose charges are equal to their masses[145]. These are also called extremal because
there is a theorem that the charges cannot exceed their masses. ...
The extremal black holes have zero Hawking temperature but nonzero Bekenstein entropy[145]....

The results in string theory do not concern, precisely, black holes, as they are found in
a limit in which the gravitational constant is turned off. But they concern systems with the
same quantum numbers as certain black holes, which, it may be argued, may become black
holes if the gravitational constant is turned up to a sufficiently strong value. Still they are
very impressive,

1. For certain compactifications, with d = 3, 4 or 5 at directions, and in the limit of
vanishing gstring, and hence GNewton, there are BPS states of string theory including D-branes, which have the same mass, charges and angular momenta of an extremal black hole in d dimensions. The number of such states is in all cases exactly equal to the exponential of the Bekenstein entropy of the corresponding black hole[146, 147, 148].

2. If one perturbs away from the BPS condition for the string theory states, to a near
extremal condition, and constructs a thermal ensemble, the spectrum of the Hawking radiation from the corresponding near extremal black hole is reproduced exactly, including the grey body factors[148].

These results are very impressive; the agreement between the formulas obtained for en-
tropy and spectra between the D-brane systems and black holes are staggeringly precise. It
is hard to believe that this level of agreement is not significant. At the same time, there are
two big issues. First the D-brane systems are not black holes. Second it has not been found
possible to extend the results away from the neighborhood of extremal, BPS states, so as
to apply to ordinary black holes.

We are then left with a conjecture:

• Black hole conjecture. If one turns the gravitational constant up in the presence
of a thermal ensemble of states which as described above, reproduce the entropy and temperature of an extreme or near extremal black hole, one can construct a string
theoretic description of quantum black hole spacetimes. This will extend also to far
from extremal black holes. [my emphasis]
..."

A more condensed summary is on page 61, where the corresponding LQG situation is also reviewed
since this is an exclusively String thread, IIRC, I will start an LQG thread about the BH entropy result
this will allow this thread to stay more on topic, hopefully

The string's length, would it not have given a determination, in terms of the energy when gathering. It would have been suitable, for blackhole gravitational consideration?

Sol

Hello Sol,
the issue which selfAdjoint brought up was the blackhole entropy consideration
which has to do with the famous Beckenstein-Hawking formula discovered in the Seventies.
There is a complete derivation applying to all BH cases in LQG which appeared in this 8-page paper by Ashtekar,Baez,Corichi,Krasnov (now known as ABCK) in 1997. I would like to get some help understanding it actually---but it does not belong in this thread.
There is also a partial derivation of the same formula in string theory! It applies in certain special cases to structures similar to electrically charged black holes with the string constant
(and thus the Newtonian gravitational constant) set equal to zero. The proof looks complicated. I think I need to focus on the LQG proof where I have some chance of gaining intuition.

Anyway the question here has to do with surface area of BH and its relation to how much diversity has been destroyed and plastered over in the forming of the BH. Think about building a parking lot that covers several square kilometers of tropical rainforest-----try to estimate all the tigers, chimpanzees, parrots and baobab trees which are destroyed by laying down the parkinglot. This is the entropy of the parking lot. Beckenstein found that it was proportional to the area of the parkinglot.

Except it was not a parkinglot but the featureless event horizon of a black hole and it was not tigers but stars that had fallen in, but you get the idea. The amazing thing is that the entropy
or amount of diversity destroyed is always equal to 1/4 of the area. this proportion 1/4
is a kind of mathematical miracle----why a simple number like 1/4?---that asks to be understood by deeper study. But I cannot discuss if further since this thread is about string
FIELD theory as compared with string theory---and I need to approach Beckenstein via loops which is different.

I am interested that Kaku claims an interest here. I don't know of any thread in the research I have seen that goes back to him, but of course that doesn't mean it isn't there.

No, you will not find his work/papers on arXiv, but you will find them on our site.

http://www.mkaku.org/articles/ [Broken] and scroll down to Academic Papers. There is enough equations in those papers to satisfy even the most devote mathematician :-)

Perhaps Dr. Kaku’s insight during one of our chat events at MKaku.org might help (which we hope to re-upload the transcripts to the site shortly):

actorgeek asked, How does M-theory differ from the original Superstring (Theory) exactly?

Dr. Kaku: They are the same theory, but M-theory is defined in 11 dimensions and has membranes, while string theory is defined in 10 dimensions and only has strings. Most of us feel that M-theory is a higher version of the same theory, such that the five known string theories can be viewed as a single theory in the 11th dimension. Think of being on a mountain top. You can see everything below as a unified whole. In the same way, the five known string theories can be seen as a single theory from the vantage point of the 11th dimension. The problem is that the 11th dimension is extremely hard to work with, while strings are very easy.

end of transcript

In regards to why M-theory is largely theoretical today and the fact that much of it has not been proven, is because it is 21st Century physics accidently discovered by 20th Century scientists. Therefore, as our ability to test the theory (probing the smallest of atomic scales, observing objects in the universe in better detail, greater understanding), M-Theory will begin to turn prediction into results:

w0rmh0lez asked, By saying no human is currently smart enough, do you mean we are missing pieces of the puzzle, if you will, or that we are having trouble unifying the theory?

Dr. Kaku: The problem is that the theory (string theory) was discovered quite by accident. We were not supposed to see this theory in this (20th) century. Perhaps in another 50 years, we might have naturally stumbled on this theory. But the theory is so strange, so bizarre, and so sophisticated, that it caught everyone by surprise. Even the mathematicians have been shocked by super string theory. New areas of math have been opened up by the theory. Usually, the mathematicians are a bit ahead of us physicists. But this time, we are far ahead of them. Hence, we don't have the tools to solve the theory. It is 21st century physics that fell into the 20th century by accident. Hence, we don't yet have the mathematical tools necessary to solve the theory. However, the equations are well defined. I found many of them myself. But the problem is that no one has the math necessary to solve them. Think of Polynesian islanders who accidentally find a TV set for the first time, fallen from an airplane. They find it is easy to turn the dials and see the TV picture. so it seems to be easy. But when they open the TV set, they find an alien science at work. In the same way, string theory or M-theory seems to be easy, being based on strings and membranes, but when we open up the back, we find a strange and beautiful mathematics that we have never been before. Maybe one you will be smart enough to solve the theory!

A string, one dimensional can be auotmatically understood in the brane? 2dimensions plus time is a way of looking at this brane and see longitudal and transvese application immediately, moving to a Z direction, time, and describing the fifth dimension.

Part of this discussion in general concerns geometry and topology. The general idea of both String Theory and Loop Quantum Field Theory is as mentioned show space-time to have its own atomic structure or rather, structure. As I've mentioned to a few before and Smolin tends to echo this these two theories share more in common than they have that strong a difference. Basically LQFT speaks about the internal or small scale structure of the strings and also the branes, while String theory in its different forms aptly discribes the effects of both the Strings and Branes along with the particle states and fields they generate.

Anyway this all goes its about the geometry and toplogy of space-time even with LQFT down to the point that our normal concepts of space and time break down. The strongest difference between the two is String Theory is background dependent while LQFT is background independent. You might say one exists in the background and the other as a composite whole generates the background.

I would like to come back to selfajoint's original question; 'How does...?'.
String-field theory is in Polchinski's words
vol II of Bjorken-Drell for string theory,
whereas Bjorken-Drell vol.I is the usual formulation
(as given in Green Schwarz and Witten e.g., or again
Polchinski, vol.I and II).
In his book Polchinski avoids string-field theory,
by the argument that all the 'new' insights (at the time of the writing of his book) had been arrived at without string-field theory.
But now there seems to be a certain renaissance of string-field theory, which is connected with the advances made by Ashoke Sen and Zwiebach, and many others who jumped in. These developments (too recent to be covered in Polchinski's books) have to do with the understanding of
tachyon dynamics, not only in bosonic string theory where they seem to appear because of inconsistencies of that framework (but the last word may not be spoken on that), but also in superstring theory. There physically reasonable tachyons do in fact appear as modes of linear instabilities of D-brane configurations which lack supersymmetry. Because of their instability such
non-BPS configurations of D-branes seemed originally to be forbidden (and are not considerd in Polchinski's books), but as dynamical and decaying states they now make sense and are most 'easily' studied (as shown by A.Sen and coworkers) in open string-field theory in the tree-approximation. (The quantum string-field theoretical description still seems to be out of reach, as far as I know, but of course I would be glad to learn otherwise).

On the technical level there seems to exist a nice and elegant string-field theory of open strings (I recommend the last sections of

Polchinski's Les Houches lecture notes 'what is string theory'

for an introduction), but the string-field theory of closed strings seems ugly, and somehow does not smell right.
The best hope seems to be that open string-field theory somehow is all we need, because open strings imply closed ones, (not the other way round, selfadjoint).
The open string-field theory looks elegant, because
it just looks like a \Phi^3 field theory, however promoted from a apace-time field to a string field,
i.e. a probability amplitude of all the classical mode-amplitudes of the mode-expansion of the open string.
Thus it's action contains a free quadratic term which
embodies the BRST operator, and the free-field equation is just the physical state condition of string theory.
The action also contains a cubic term, which, very nontrivially, is all one needs to account for the complete world-sheet genus-expansion of open string-theory. This expansion must contain the closed strings as intermediate states.
I think (i.e. hope) it is a framework which still harbours a lot of surprises, in particular in its quantised version

Closed string field theory on the other hand is ugly, because it needs interaction vertices to all orders, thus it looks like a foreign structure artificially forced on a theory, which is more economically desribed by other means. (Like the time-honoured epicycles, which are not wrong, but uneconomical).